Reformulation of stochastic dynamic control and filtering problems via a change of measure has proven to be very effective for existence, approximations, filtering, and dynamic programming methods under a variety of contexts. In discrete-time, such a formulation leads to an equivalent system under which measurements are exogenous independent variables. For continuous-time stochastic control, this method has been very popular since the analysis in [1]}, to avoid stringent conditions on control policies to satisfy the existence of strong solutions to controlled stochastic differential equations (see also [2]}, [3]}), which allows the control to be a function of an independent Brownian innovations process. This was utilized by Fleming and Pardoux [4]}, who introduced wide-sense admissible control policies for classical partially observed stochastic control problems (POMDPs), where first the measures were reduced to an exogenous Brownian process and a control policy was defined to be wide-sense admissible if the control and (exogenous) measurements were independent from future increments of the measurement process (see also [5]}, where this was utilized further without separating estimation and control in POMDPs). Borkar [6]}, [7]} obtained existence results in average cost POMDPs via generalizing Fleming and Pardoux's notion to discrete-time POMDPs, where, once again, first the measurements were made independent and then the control and measurements form a wide-sense admissible process if they are independent from future measurements. In non-linear filtering theory such methods have found applications via the Kushner-Kallianpur-Striebel formula [8]}.
